What Generator for a 15000BTU AC unit?

Having owned a Honda EU3000is, I can tell you that your Honda will not run everything! Many years ago, I opened up my brand new $1400 Honda EU300is (I told you many years ago). Oiled and fueled it up and dragged the wife out to the front yard to watch it fire up the 13,6k A/C on our trailer. It was about 95 degrees outside. I unplugged the land line from the garage, fired up the Honda, turned off the Eco mode switch and then turned on the trailer's A/C. It couldn't handle the load. So, relaxing in my new room under a tarp in the back yard, searching this very forum, I discovered the hard start kit. Info about it had been offered up by another Honda owner who was most likely sleeping in his back yard. Put that in and the Honda would finally run the A/C. I was able to move back inside.
Long story short, don't count on it. If you're going to go with the more expensive solutions, rent one from a local rental yard and try it out first. Sleeping in the back yard in the summer in Central California is not fun.